Method for operating a photonic circuit

Abstract

The invention relates to a method for operating a photonic circuit (50), in particular a photonic quad-rail gate, for generating entangled light states (1-8), which comprises steps for periodically generating several spatially separated squeezed light states (1-8), for spatially separating the squeezed light states (1-8) into the photonic circuit (50), for converting the squeezed light states (1-8) into EPR pairs in pairs, and for applying at least one time-division multiplexing operation to at least two EPR pairs, in particular to two light states (1-8) of different EPR pairs, to generate an entangled cluster state.Four light states (1, 2, 3, 8; 4, 5, 6, 7) are entangled with each other by means of beam splitter interactions such that at least one spatial quad-rail gate node (17) is created, wherein the at least one spatial quad-rail gate node (17) is formed from a non-time-shifted light state (1, 5) of a first EPR pair, a time-shifted complementary light state (2, 6) of a temporally earlier identical EPR pair, a non-time-shifted light state (3, 7) of a second EPR pair and a non-time-shifted light state (8, 4) of a third EPR pair.

Description

[0001] The application relates to a method for operating a photonic circuit to generate entangled light states. Further aspects of the invention include a photonic circuit and a quantum computer.

[0002] Photonic circuits, which are used to entangle generated light states, are well-known. Light states entangled by such photonic circuits are used particularly in quantum computers. These circuits are generated using free-space optics (FSO) setups. These consist of either only temporal or only spatial multiplexing. This technique is space-intensive and therefore cannot be used in integrated photonic circuits.

[0003] Maintaining phase stability in this technique is also very difficult, as free-space structures are highly susceptible to mechanical and other disturbances. However, sufficient phase stability is a fundamental requirement for quantum computing applications.

[0004] Furthermore, known free-space configurations only generate a limited amount of entanglement, which cannot be directly scaled to larger systems. Scalability beyond a few qubits is therefore not possible with current technology, meaning that existing photonic circuits are not suitable for photonic quantum computers.

[0005] The D1 paper describes how, due to its unique scaling potential, continuously variable quantum optics is a promising platform for large-scale quantum computing. In particular, very large cluster states with a two-dimensional topology suitable for universal quantum computing and quantum simulation can be deterministically generated. Furthermore, approaches for fault tolerance through bosonic quantum error correction are known.

[0006] This article proposes a complete, measurement-based quantum computing architecture for implementing a universal gate mentor set on the recently generated two-dimensional cluster states. The performance of various quantum gates operating in these cluster states, as well as in other two-dimensional cluster states (such as the double-layer square lattice and the four-rail lattice cluster state), is analyzed by estimating and minimizing the associated stochastic noise and the resulting gate failure probability.

[0007] The four different states are compared and it is found that, although they all allow universal computations, the four-rail grid cluster state shows better performance than the other three states, which all have similar performance.

[0008] D1: LARSEN, Mikkel V. ; NEERGAARD-NIELSEN, Jonas S. ; ANDERSEN, Ulrik L.: Architecture and noise analysis of continuous-variable quantum gates using two-dimensional cluster states. Preprint. [v2] Tue, 20 Oct 2020 08:04:22 UTC. 2020-10-20. pp. 1-26. https: / / doi.org / 10.48550 / arXiv.2005.13513 [accessed on 2025-09-23]

[0009] The object of the present invention is therefore to provide a method for entangling light states which is suitable for photonic quantum computers.

[0010] This problem is solved in a method for operating a photonic circuit, in particular a photonic quad-rail gate, of the type mentioned above, by the fact that the method includes steps for the periodic generation of several spatially separated squeezed light states, for the spatially separate feeding of the squeezed light states into the integrated photonic circuit, for the pairwise conversion of the squeezed light states into EPR pairs (Einstein-Podolsky-Rosen pairs) and for the application of at least one time-division multiplexing operation on at least two EPR pairs, in particular on two light states of different EPR pairs, to generate an entangled cluster state.Four light states are entangled with each other by means of beam splitter interactions such that at least one spatial quad-rail gate node is created, wherein the at least one spatial quad-rail gate node is formed from a non-time-shifted light state of a first EPR pair, a time-shifted complementary light state of a temporally earlier identical EPR pair, a non-time-shifted light state of a second EPR pair and a non-time-shifted light state of a third EPR pair.

[0011] In the periodic generation of multiple spatially separated squeezed light states, several spatially separated squeezed light states are generated at a single point in time. The same squeezed light states are then generated again after a predefined period, resulting in spatially separated temporal sequences of identical squeezed light states. The squeezed light states generated at temporal intervals are therefore identical, whereas spatially separated squeezed light states can also be non-identical. Non-identical light states can differ, for example, in their (average) number of photons and / or their orientation in phase space and / or exhibit different levels of squeeze.

[0012] The squeezed light states exhibit a certain degree of squeezing in their phase-space quadrature. In this way, the light states can lead to a cluster state, which is suitable for CV quantum computing (continuous-variable quantum computing), since CV quantum computing requires a multimodal squeezed Gaussian state as a resource state.

[0013] Before being fed into the photonic circuit, the squeezed light states can be filtered so that the most interference-free squeezed light states possible are fed into the photonic circuit, especially for use in a quantum computer.

[0014] The spatially separated injection of the squeezed light states can, for example, be achieved into different and separate waveguides within the circuit. These waveguides can be part of a photonic chip. In this way, the space requirement can be reduced, particularly by a factor of more than 100 compared to conventional free-space setups. The photonic circuit can thus be designed as an integrated photonic circuit and, in particular, fully integrated into a photonic chip.

[0015] In the circuit, the squeezed light states can be converted pairwise into EPR pairs, i.e., Einstein-Podolsky-Rosen pairs, also called Bell states. The conversion of two squeezed light states into an EPR pair can be easily accomplished using a beam splitter, which entangles the two squeezed light states. The phase-space orientation of the two squeezed light states can be varied, particularly by means of a phase shifter. Specifically, a p-squeezed light state can be converted into an EPR pair with a q-squeezed light state via a beam splitter interaction, especially after one of the light states has undergone a 90-degree phase shift.

[0016] Using time-division multiplexing, at least two EPR pairs can be entangled, wherein the EPR pairs, or at least one light state of the EPR pairs, are temporally separated from each other. Preferably, this time-division multiplexing can be performed by entangling two light states of two EPR pairs that are not temporally separated from each other, wherein at least one of the remaining light states of the two EPR pairs, in particular the two remaining light states of the two EPR pairs, is temporally separated from the two light states that are not temporally separated from each other and / or from each other.

[0017] By combining spatial and temporal multiplexing, a large entangled cluster state can be generated using different squeezed light states. Furthermore, improved phase stability and long-term stability can be achieved compared to free-space setups. This results in an entanglement of light states suitable for photonic quantum computers.

[0018] In this context, it has proven advantageous to time-shift at least one light state of at least one EPR pair relative to the other light state of the EPR pair. Time-division multiplexing can be easily achieved by shifting at least one light state of the at least one EPR pair. Preferably, the light states of several, in particular two, unequal EPR pairs are time-shifted. Two EPR pairs are unequal if the light states of one EPR pair are not the same as the light states of the other EPR pair. The photonic circuit can incorporate delay lines to generate the time-shifted EPR states.

[0019] In a further development of the invention, the at least one time-shifted light state of the at least one EPR pair is entangled with the complementary light state of a temporally later identical EPR pair. This entanglement allows for the simple application of a time-division multiplexing operation to two EPR pairs. A complementary light state is defined as the second light state that, together with a first light state (e.g., the time-shifted light state) or a light state identical to the first light state, i.e., a light state generated in the temporal sequence before or after the first light state but otherwise identical, forms an EPR pair. Two EPR pairs are identical if the light states of one EPR pair are identical to the light states of the other EPR pair.

[0020] According to one embodiment, it is proposed that four light states are entangled with each other by means of beam splitter interactions such that at least one spatial quad-rail gate node is created. Within a spatial quad-rail gate node, four unentangled and spatially separated light states can be transformed into four entangled and still spatially separated light states. The entanglement of the four light states by means of beam splitter interactions can be configured such that each light state is entangled with at least two other light states. Preferably, each of the four light states belongs to a different EPR pair. More preferably, light states from at least three dissimilar EPR pairs are entangled with each other to generate the at least one spatial quad-rail gate node.A photonic circuit with a quad-rail gate node can represent a quad-rail gate in which four light states are entangled.

[0021] Preferably, the photonic circuit comprises two spatial quad-rail gate nodes. Preferably, eight light states are fed into the photonic circuit and converted into four unequal EPR pairs. A photonic circuit with two quad-rail gate nodes can represent a quad-rail gate in which eight light states are converted into two groups of entangled light states.

[0022] In a further development of the invention, it is proposed that the at least one spatial quad-rail gate node is formed from a non-time-shifted light state of a first EPR pair, a time-shifted complementary light state of an earlier identical EPR pair, a non-time-shifted light state of a second EPR pair, and a non-time-shifted light state of a third EPR pair. In this way, it is sufficient to time-shift only one light state to generate the quad-rail gate node. Advantageously, both light states of the second and / or third EPR pair are non-time-shifted.

[0023] In this context, it has proven advantageous to entangle the time-shifted light state of the EPR pair identical to the first EPR pair and / or the non-time-shifted light state of the third EPR pair of the at least one spatial quad-rail gate node with the non-time-shifted light state of the first EPR pair and the non-time-shifted light state of the second EPR pair, respectively. In particular, the identical EPR pairs with a time-shifted light state can thus be connected to the other EPR pairs of the quad-rail gate node, especially those without a time-shifted light state.

[0024] According to a preferred embodiment, the at least one spatial quad-rail gate node is time-division multiple times. This time-division multiplexing can be achieved by entangling several light states of the spatial quad-rail gate node, in particular at least one light state of each EPR pair, with a time-shifted light state of the same spatial quad-rail gate node. Two time-spaced quad-rail gate nodes can thus be interconnected via the time-shifted and non-time-shifted light states of the same EPR pair. This interconnection can be configured such that the non-time-shifted light state of the EPR pair is part of a first spatial quad-rail gate node, while the time-shifted complementary light state of the same EPR pair is part of a later second quad-rail gate node.Multiple time-division multiplexing can be achieved by entangling a light state of the spatial quad-rail gate node with a non-time-shifted light state complementary to the time-shifted light state of the EPR pair corresponding to the EPR pair of the time-shifted light state. This complementary non-time-shifted light state can connect the spatial quad-rail gate node to another spatial quad-rail gate node spaced in the opposite time direction. In this way, a connected temporal chain of spatial quad-rail gate nodes can be generated, which can be continued in both time directions.

[0025] It is possible that at least one light state is phase-shifted between two beam splitter interactions. This phase shift between two beam splitter interactions allows the phase of the light state to be corrected or selectively changed. The phase shift can be achieved by a phase shifter in the photonic circuit. The phase shifter can be positioned between two beam splitters in the photonic circuit.

[0026] In a further embodiment of the invention, quadrature values ​​encoded in the squeezed light states are measured at the end of the photonic circuit using homodyne detection. The state values ​​at the end of the photonic circuit can be easily read out using homodyne detection to obtain the result of quantum computing.

[0027] In this context, it has proven advantageous to generate interference between the respective light state at the end of the photonic circuit and a reference radiation, particularly by means of a tunable directional coupler, preferably set to a 50 / 50 split ratio, and to use this interference together with the reference radiation for homodyne detection. In this way, suitable signals for detection and evaluation can be generated. The interferences generated from the individual light states, particularly by means of the directional coupler, are fed to detectors via detector outputs of the photonic circuit in parallel with the reference radiations. The detectors, particularly symmetrical ones, can detect intensity differences between two detector outputs assigned to a single light state, in particular between the interference and reference radiation associated with that light state.

[0028] The reference radiation can be easily generated using an external local oscillator connected to the squash-generating lasers. This allows the reference radiation to be matched to the specific laser radiation used to squash the original light state. The phase of the local oscillator can be adjusted using fast phase shifters, each assigned to one of the squash-generating lasers. These fast phase shifts can be induced in an InP chip via electro-optical modulation to generate and emit the reference radiation.

[0029] Preferably, a measured intensity difference is integrated over a predefined time interval. In this way, statistical quantum properties can be determined. The resulting quadrature can be measured, in particular, by convolution with a response function.

[0030] According to one embodiment of the invention, it is proposed that at least one detector output be routed to a photon-number resolving detector, in particular a PNR-SNSPD or TES. A PNR-SNSPD (photon-number resolving superconducting nanowire single-photon detector) or a TES (transition edge sensor) can enable reliable and accurate photon-number resolving measurements. By performing a photon-number resolving measurement at this detector output, the implementation of, in particular, cubic non-Gaussian gates can be enabled.

[0031] In the case of a photonic circuit, in particular an integrated circuit, of the type mentioned above, it is proposed to solve the above problem by designing it to carry out the previously described method, thereby yielding the advantages described in connection with the method.

[0032] The features described in connection with the method according to the invention can also be applied individually or in combination to photonic circuitry. The same advantages arise as already described.

[0033] According to a proposed design, the photonic circuit comprises at least four quad beam splitters to generate a spatial quad-rail gate node. This circuit can have four inputs, each representing a different light state. In particular, the circuit can be multi-stage.

[0034] A first stage of the circuit can have two quad beam splitters, whose inputs form the four inputs of the circuit.

[0035] A second stage of the circuit can include two further quad beam splitters, the first input of each of which is connected to an output of the first quad beam splitter of the first stage, and the second input of each of which is connected to an output of the second quad beam splitter of the first stage. The inputs of the quad beam splitters of the second stage can thus be connected to different outputs of different quad beam splitters of the first stage.

[0036] Phase shifters can be connected downstream of the outputs of the quadruple beam splitters of the first stage and / or the outputs of the quadruple beam splitters of the second stage. The outputs of the quadruple beam splitters of the first stage and the inputs of the quadruple beam splitters of the second stage can be connected via the phase shifters connected downstream of the quadruple beam splitters of the first stage.

[0037] Preferably, the photonic circuit can comprise two parallel interconnections of four quad beam splitters to generate two spatial quad-rail gate nodes. This can enable the simple generation of a spatial quad-rail gate node.

[0038] In the case of a quantum computer of the type mentioned above, it is proposed to solve the above problem that it be configured to carry out the previously described method and / or have a photonic circuit configured in the manner described above, thereby yielding the advantages described in connection with the method and the photonic circuit.

[0039] The features described in connection with the inventive method and the photonic circuit can also be applied individually or in combination to the quantum computer. The same advantages arise as already described.

[0040] The following section explains embodiments, further developments, and examples of the invention in more detail with reference to the accompanying drawings. The figures show: Fig. 1 a schematic structure of the generated cluster state and Fig. 2 a schematic diagram of the photonic circuit for carrying out the procedure.

[0041] In Fig. Figure 1 shows the schematic structure of the cluster state generated by the method according to the invention, which is achieved at the end of the photonic circuit 50. This state consists of several spatially separated squeezed light states 1-8, i.e., they are spatially separated from each other and also propagate separately from each other through the photonic circuit 50. These spatially separated light states 1-8 only interact with each other in the quadruple beam splitters 11 described below.

[0042] Light states 1-8 are generated at periodic intervals, resulting in a temporal sequence of identical light states 1-8. For example, light state 1 is generated at an initial point in time. After a predetermined period, the same light state 1 is generated again.

[0043] This temporal sequence of spatially separated light states 1-8 is incorporated into the Fig. The light is fed into the waveguide 9 of the photonic circuit 50 shown in the two images. The circuit 50 has its own waveguide 9 for each of the spatially separated light states 1-8, so that the light states 1-8 remain spatially separated even when passing through the photonic circuit 50.

[0044] In the photonic circuit 50, each pair of these light states 1-8 is converted into an EPR pair. Fig. 1 This is symbolized by the thick connecting line between the light states 1, 2; 3, 4; 5, 6; 7, 8.

[0045] To generate these EPR pairs, the light states 1-8 in a first section A of the circuit 50 are each directed into an input of a quadruple beam splitter 11, so that one pair of light states 1-8 is entangled with each other. The two light states 1-8 of these EPR pairs exit the quadruple beam splitter 11 at its outputs. The respective phase of the light states 1-8 can be adjusted by means of a downstream phase shifter 12.

[0046] In the first region A of the photonic circuit 50, the waveguides of the two light states 2 and 6 each additionally have a delay line 10. This delay line 10 shifts the light states 2 and 6 in time. Meanwhile, the complementary light states 1 and 5 of the EPR pairs formed by the light states 2 and 6 are not shifted in time.

[0047] In Fig. This time shift between light states 2 and 6 can be seen in Figure 1 by the fact that these are represented along the time axis T at time t2, while the other light states 1, 3, 4, 5, 7, 8, which are fed into circuit 50 together with them, are represented at time t1. The thick line symbolizing the EPR pair runs accordingly between light states 1 and 2 and light states 5 and 6. Fig. 1 horizontal, while for the EPR pairs consisting of two non-time-shifted light states 3, 4, 7, 8 it runs vertically.

[0048] The time shifts caused by the delay lines 10 are synchronized with the period of generation of the spatially discriminated light states 1-8 such that light states 2 and 6 are shifted by one period. At the end of the first section A of the circuit 50, the time-shifted light states 2 and 6 therefore arrive at time t2 together with the subsequently introduced light states 1, 3, 4, 5, 7, and 8, although these remain spatially separated. The light states 1, 3, 4, 5, 7, and 8, which were introduced together with the time-shifted light states 2 and 6, have already reached the end of the first section A at time t1. In contrast, the light states 2, 6, which are fed in together with the later fed-in light states 1, 3, 4, 5, 7, 8, which reach the end of the first area A at time t2, are also time-shifted, so that they only reach the end of the first area A at time t3.

[0049] Light states 1, 3, 4, 5, 7, 8 now enter the second region B of the photonic circuit 50 together with the time-shifted light states 2, 6. This circuit has two interconnections 15 consisting of quad beam splitters 11, which serve to generate quad-rail gate nodes 17. At the quad-rail gate nodes 17, light states 1-8 are entangled with each other across the EPR pairs by beam splitter interactions. The two interconnections 15 are connected in parallel.

[0050] Both circuits 15 each have two stages consisting of two parallel-connected quadruple beam splitters 11.

[0051] In the Fig. In the first circuit shown on the left, light state 1 is entangled with the time-shifted light state 2 in the first stage. This entanglement through a beam splitter interaction is possible because light state 1 and the time-shifted light state 2 are not temporally separated from each other. Light state 1 (at time t1), which forms an EPR pair with the time-shifted light state 2, and light state 2, which is time-shifted towards time t3 and forms an EPR pair with light state 1 (which is entangled with the time-shifted light state 2 at time t2), are temporally separated from the two light states 1 and 2 entangled at time t2 by a beam splitter interaction.This results in time-division multiplexing, in which light state 1 is linked via the time-shifted light state 2 to the temporally preceding light state 1, which forms an EPR pair with the time-shifted light state 2. The entanglement of light state 1 with the time-shifted light state 2 is described in . Fig. 1 is symbolized by a thinner connecting line between light states 1 and 2 at time t2. The connection between light state 1 at time t2 and light state 1 at time t1 can be traced by the connection via the solid lines. This also applies to light state 2 at time t3, which is also shifted in time.

[0052] In parallel, in the first stage of the first circuit 15, light state 3 is entangled with light state 8 by a beam splitter interaction. In this process, two non-time-shifted light states 3 and 8 of unequal EPR pairs are entangled with each other.

[0053] In the second stage of the first circuit 15, the light state 1 coming from the left output of the left quadruple beam splitter 11 of the first stage is entangled with the light state 8 coming from the right output of the right quadruple beam splitter 11 of the first stage. In the same way, the time-shifted light state 2 coming from the right output of the left quadruple beam splitter 11 of the first stage is entangled with the light state 3 coming from the left output of the right quadruple beam splitter 11 of the first stage.

[0054] At the end of the second section B of circuit 50, the following is thus established: Fig. Figure 1 shows the entanglement of light states 1, 2, 3, and 8. In this configuration, two light states 3 and 8 of two dissimilar EPR pairs, formed by non-time-shifted light states 3, 4, 7, and 8, are connected to two light states 1 and 2 of identical EPR pairs, one of which is time-shifted. This creates a quad-rail gate node that connects four EPR states, one of which spans the time domain.

[0055] Similarly, in the first stage of the Fig. In the second circuit shown on the right, 15, the non-time-shifted light state 4 is first entangled with the non-time-shifted light state 5 by a quadruple beam splitter 11. In parallel, the time-shifted light state 6 is entangled with the non-time-shifted light state 7.

[0056] In the second stage of the second circuit 15, the light state 4 coming from the left output of the left quadruple beam splitter 11 of the first stage is entangled with the light state 7 coming from the right output of the right quadruple beam splitter 11 of the first stage. In the same way, the light state 5 coming from the right output of the left quadruple beam splitter 11 of the first stage is entangled with the time-shifted light state 6 coming from the left output of the right quadruple beam splitter 11 of the first stage.

[0057] In the illustrated embodiment of the photonic circuit 50, a phase shifter 12 is arranged in the waveguide 9 behind each output of a quadruple beam splitter 11.

[0058] At the end of the second section B of the photonic circuit 50, the following also arises: Fig. Figure 1 shows the entanglement of light states 4-7. In this configuration, two light states 4, 7 of two unequal EPR pairs, formed by non-time-shifted light states 3, 4, 7, 8, are connected to two light states 5, 6 of identical EPR pairs, one of which is time-shifted. In this way, the quad-rail gate node 17 is formed, which connects four EPR states, one of which spans the time domain. This quad-rail gate node 17 is shown in Fig. 1 highlighted with a circle surrounding it.

[0059] While the EPR pairs with time-shifted light states 2, 6 connect several quad-rail gate nodes 17 in the time domain, the EPR pairs which do not have time-shifted light states 2, 6 connect several quad-rail gate nodes 17 in the space domain.

[0060] Based on the in Fig.Figure 1, showing the cluster state after traversing sections A and B of the photonic circuit 50, demonstrates that this circuit 50 can generate a large entangled cluster state from a multitude of EPR states. These entanglements are not limited to spatial entanglements but also connect time-displaced light states via the EPR pairs with time-shifted light states 2, 6. This combination of spatial and temporal multiplexing enables the generation of large entangled cluster states with a large number of entanglements, which are directly scalable to larger systems. The photonic circuit 50 can be easily adapted to a larger system by increasing the number of interconnections 15 or by interconnections 15 with additional stages.

[0061] In a final section C, the photonic circuit 50 has several directional couplers 13. The waveguides 9, corresponding to the light states 1-8, each terminate in such a directional coupler 13. In addition to the respective light state 1-8, a reference radiation is supplied to the respective directional coupler 13. The reference radiation is generated by a local oscillator 16, to which eight fast phase shifters (not shown) are connected to change the phase of the local oscillator 16 and are connected to the lasers (not shown) that generate the squeezed light states 1-8. These fast phase shifts are induced by electro-optic modulation in an InP chip, which emits the respective reference radiation. This radiation is guided via an optical fiber to the respective directional coupler 13.

[0062] The interference of the squeezed light and the local oscillator generated by the respective directional coupler 13 is output via the detector outputs 14, to which, for example, homodyne detectors, TES or PNR-SNSPD can be connected to measure the light states 1-8 of the cluster state. REFERENCE MARK LIST 1-8 light states 9 waveguides 10 Delay line 11 quadruple beam splitters 12 phase shifters 13 directional couplers 14 Detector output 15 Wiring 16 Oscillator 17 Quad-Rail Gate Nodes 50 photonic circuits t1-t3 time points Area Area B C area T Time axis

Claims

[1] Method for operating a photonic circuit (50), in particular a photonic quad-rail gate, for generating entangled light states (1-8) comprising the steps: • Periodic generation of several spatially separated squeezed light states (1-8); • spatially separated feeding of the squeezed light states (1-8) into the photonic circuit (50); • pairwise conversion of the squeezed light states (1-8) into EPR pairs; • Application of at least one time-division multiplex operation to at least two EPR pairs, in particular to two light states (1-8) of different EPR pairs, to generate an entangled cluster state; characterized by, that four light states (1, 2, 3, 8; 4, 5, 6, 7) are entangled with each other by means of beam splitter interactions such that at least one spatial quad-rail gate node (17) is created, wherein the at least one spatial quad-rail gate node (17) is formed from a non-time-shifted light state (1, 5) of a first EPR pair, a time-shifted complementary light state (2, 6) of a temporally earlier identical EPR pair, a non-time-shifted light state (3, 7) of a second EPR pair and a non-time-shifted light state (8, 4) of a third EPR pair. [2] Method according to claim 1, characterized by , that at least one light state (2, 6) of at least one EPR pair is time-shifted relative to the other light state (1, 5) of the EPR pair. [3] Method according to claim 2, characterized by, that the at least one time-shifted light state (2, 6) of the at least one EPR pair is entangled with the complementary light state (1, 5) of a temporally later identical EPR pair. [4] Method according to claim 1, characterized by , that the time-shifted light state (2, 6) of the EPR pair identical to the first EPR pair and / or the non-time-shifted light state (4, 8) of the third EPR pair of the at least one spatial quad-rail gate node is entangled with the non-time-shifted light state (1, 5) of the first EPR pair and the non-time-shifted light state (3, 7) of the second EPR pair. [5] Method according to any one of the preceding claims 1 to 4, characterized by , that the at least one spatial quad-rail gate node (17) is time-multiplexed multiple times. [6] Method according to any one of the preceding claims 1 to 5, characterized by, that at least one light state (1-8) is phase-shifted between two beam splitter interactions. [7] Method according to any one of the preceding claims, characterized by , that quadrature values ​​encoded in the squeezed light states (1-8) are measured using homodyne detection at the end of the photonic circuit (50). [8] Method according to claim 7, characterized by , that an interference of the light states (1-8) at the end of the photonic circuit (50) and a reference radiation is generated, in particular by means of a tunable directional coupler (13), preferably set to a split ratio of 50 / 50, and is used together with the reference radiation in homodyne detection. [9] Method according to any one of the preceding claims 7 or 8, characterized by that a measured intensity difference is integrated over a predefined time interval. [10] Method according to any one of the preceding claims, characterized by , that at least one detector output (14) is directed to a photon-number resolving detector, in particular a PNR-SNSPD or TES. [11] Photonic circuit (50), in particular integrated photonic circuit, which is designed to carry out the method according to any one of claims 1 to 10. [12] Photonic circuit (50) according to claim 11, characterized by at least one interconnection (15) of four quad beam splitters (11) to generate a spatial quad-rail gate node (17). [13] Quantum computers, characterized by that it is configured to carry out the method according to one of claims 1 to 10 and / or comprises a photonic circuit (50) according to one of claims 11 or 12.

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